Search

The feedback circuit approach to nonlinear dynamical systems pioneered by Thomas and coworkers is revisited in a thermodynamical perspective. The role of nonequilibrium conditions and of other types of constraints such as mass action kinetics or microscopic reversibility around thermodynamic equilibrium in the way positive feedback circuits are operating is analyzed. It is shown that the appearance of non-trivial steady-state and time-dependent behaviors necessitates that the strengths of the feedback loops present exceed some well-defined critical values. Illustrations are provided on prototypical systems giving rise to multiple steady states., (Copyright © 2018. Published by Elsevier Ltd.)

In a previous study, the early stages of self-assembly in nanophase materials were explored by coupling a kinetic mean-field analysis with a lattice-based stochastic theory [J. J. Kozak et al., J. Chem. Phys. 126, 154701 (2007)]. Recent experimental results on the postnucleation stages of zeolite assembly and protein crystallite formation have suggested a new study, presented here, in which the docking of a platelet on the existing surface of a structured crystallite is similarly investigated. A model is designed which allows the quantification of factors affecting docking efficiency; principal among these is the structure of the template itself, which here is assumed to be either unstructured or bifurcated into terraces and edges/ledges. Going beyond our earlier study (in which diffusion was restricted to d=2 dimensions), the diffusion space here is enlarged to consider both d=2 and d=3 dimensional flows. By expanding the external diffusion space systematically, we are able to document the consequences (as regards docking efficiency) of diffusive flows in the near neighborhood of a developing crystallite versus surface-only processes. Particularly in regimes where the barriers to surface diffusion are high, and/or the probability of desorption significant, we find that d=3 dimensional processes (leading to a "direct hit") can compete kinetically with surface-only mediated processes. Although the crystallite model studied here is simple, it can be diffeomorphically distorted into a manifold of possible geometries; in analogy with the classical theory of corresponding states, we argue that the familial relationship among these structures suggests that the generic results obtained provide a qualitatively correct description of the kinetics of docking on structured surfaces.

Evaluates thermodynamic entropy production in different parts of the attractor of two representative reactive models giving rise to periodic and chaotic behavior. Variability patterns observed as the system runs over the attractor; Comparison with the variability of indicators of the intrinsic complexity of the dynamics such as the local Lyapunov exponents.

The stochastic analysis of a chemical system obeying to mass-action kinetics and giving rise to deterministic chaos is carried out using the master equation approach. Quantitative comparison with the predictions of the deterministic description based on the rate equations shows that the system’s attractor and the probabilistic properties are robust toward fluctuations. [ABSTRACT FROM AUTHOR]

We show that simple diffusive systems, such as the Lorentz gas and multibaker maps, are perfectly compatible with the laws of irreversible thermodynamics, despite the fact that the moving particles, or their equivalents, in these models do not interact with each other, and that the dynamics takes place in low-dimensional phase spaces. The interaction of moving particles with scatterers provides the dynamical mechanism responsible for an approach to equilibrium, under appropriate conditions. This analysis provides a refutation of the criticisms expressed recently by Cohen and Rondoni (Physica A 306 (2002) 117). [Copyright &y& Elsevier]